I find kuzushi from katate dori the hardest as static. Also some schools break up (float) down (as per sumi otoshi).

I find that kaitennage is hard for many people because the tai sabaki is visually deceptive especially in ki no nagare (flowing) practice. Many times it is performed with this big tai no henko, a floor sweeping cut as you step-turn irimi and then come up for the irimi throw. Many do teach kaitennage as flowing from the beginning, and it is meant to be flowing in its actual application.

There is, however, a kihon underlying all that that may help some people to get it sooner early on. I find the following description of one of the kihon waza variations is sometimes more helpful to understand initially. If your instructors say different -- do what they say, for the love of Pete. They can see you. I can't.

For those unfamiliar with turn terminology -- the soto (outside) turn opens the book -- uchi (inside) turn closes the book. The covers (uke/ nage) are opening from a hinge at the point of connection in the soto turn -- the uchi turn is where the covers are closing on one another from the connection hinge. "Inside" turn and "outside" turn can be a ltittle difficult to see as such in actual practice.

Kaitennage can be done with only little tenkan hip turns and minimal foot movement. These illustrate the basic complexity of the technique that is only a barely perceptible (but critical) set of burbles in the more flowing version. I find students tend to get caught up in the hands and feet and for this reason concentration on more basic (irimi/tenkan) body movement (tai-sabaki) is helpful -- as is figuring out how you would perform the movement with a sword.

Attack is katatedori. Emphasis must be placed on performing the movement at full arm extension throughout (no "arm-pumping").

First, step in to the ura side with an irimi tenkan (soto) but do not put the foot back as in tai no henko. (i.e. --if he stepped in on the left foot you are now facing the same way with your left foot also forward and weight on your rear leg.) Kokyu for the leading (low) hand is rotating in and down, initially, (as for tenchinage). Kuzushi should occur if you have extended through his grab in the turn.

Second, another tenkan (uchi) -- without moving the feet, open the hips toward him (heel pivot) and move as though in a sweeping gedan or do sword cut with the gripped hand to the legs or belly, raising the (free) left hand (as in tenchinage), and address his center to your front. (If you irimi on the high hand side at this point it IS tenchinage.)

Third, entering slightly with the hips setting the weight on the forward leg (but without stepping) cutting the back of the neck yokomenuchi with the high hand, finish cutting the gedan sweep of the gripped hand -- turn the hips tenkan (soto) as you are cutting as you would in a pivoting draw cut shifting weight again to the back leg, again opening the hips strongly (heel pivot), -- reverse the high/low position of the hands as both cuts are completed -- allowing the direct irimi step across his front for the throw.

If you visualize holding an O-dachi with its tsuka the length of the distance between nage's hand on uke's neck and nage's extended arm holding uke's arm across his back, you can see the cutting position in the tai-jutsu You can see it even more dramatically if you perform the finishing move by continuing the cut of the head with full extension on the uke's braced arm, shuffle step to the same hanmi as the throw but then drop first to the knee near the head, straight down (not backing up or going forward ) and then the other knee to the suwari pin between your knees. Please do this VERRRY slowy for uke's sake.

Visualize (or get a bokken and try it) beginning with his hand gripping your right sword hand on the inside, sword open to the right. (For those that have done Saotome's bukiwaza this basically uchitachi's finishing position in kumitachi 1-4)

The initial irimi and tenkan soto turn cuts the belly laterally, right to left (as nage/shitachi views it).

The kokyu turn of the hand down and in after you turn opens the blade in reverse to cut the belly or legs on the return tenkan uchi -- cutting laterally or underneath, left to right.

The reversal of the hands, top and bottom, in the soto turn allows uke's head to be cut down in kuzushi and the sword to come up and over cutting to take the head in the final irimi cut.

If you try this with the bokken and use the tai-sabaki described you will make some better sense of the tai-jutsu. Trying to learn it in flowing mode to begin with can be frustrating for many people, and they may not recognize the crucial changes in the body movement that are obscured in ki no nagare practice. Varying the order and direction of the turns and entries allows tai sabaki variations (at least sixteen) and the movements are often so implicit in ki no nagare you may not notice them until much later on. (I know I didn't.)